November 22, 2004
Problem of the Month

Chocolate Squares
by Dr. Alexander Bogomolny

If you have a chocolate bar consisting of squares arranged in a rectangular pattern -- say 2 x 5 squares. Your task is to split the bar into small 1 x 1 squares (always breaking along the lines between the squares) with a minimum number of breaks (you may not lift up pieces and place them on top of each other).

How many breaks will it take to break up a 2 x 5 chocolate bar into 1 x 1 squares?

If the chocolate bar has m row by n columns, what is the minimum number of breaks needed to split it into 1 x 1 squares?

Solution to the Problem:

The answer is 9 breaks for the 2 x 5 bar and (m) (n) - 1 for the m x n bar.

It always takes one less than the number of chocolate squares.

Click here for a puzzle about chocolate math!

Correctly solved by:

1. Tristan Collins	Winchester, Virginia
2. Walt Arrison	Philadelphia, Pennsylvania
3. Emily Auerbach	Columbus, Georgia
4. Mandy Auerbach	Columbus, Georgia
5. Keith Mealy	Cincinnati, Ohio
6. James Alarie	University of Michigan -- Flint, Flint, Michigan
7. Tyler Windham	Columbus, Georgia
8. John Funk	Ventura, California
9. Dave Smith	Toledo, Ohio
10. Jason LaRusso	Winchester, Virginia
11. Cameron S.	Columbus, Georgia
12. Jim Kennedy	Limerick, Ireland
13. Arin Smith	Winchester, Virginia
14. Jeffrey Gaither	Winchester, Virginia
15. Jaime Garcia-Ramirez	Virginia Tech, Blacksburg, Virginia
16. John Beasley	Lord Fairfax Community College, Middletown, Virginia
17. David & Judy Dixon	Bennettsville, South Carolina
18. Jonas Sutinen	Tullängsskolan, Hällefors, Sweden
19. Anders Johansson	Tullängsskolan, Örebro, Sweden
20. Per Björkil	Tullängsskolan, Örebro, Sweden
21. Tobias Flodmark	Tullängsskolan, Örebro, Sweden
22. Gustav Nilsson	Tullängsskolan, Örebro, Sweden
23. Erik Hultgren	Tullängskolan, Örebro, Sweden
24. Jonathan Jansson	Örebro, Tullängensskola, Sweden
25. Joakim Berggren	Örebro, Tullängskolan, Sweden
26. Stehr Ako	Örebro, Tullängskolan, Sweden
27. Erik Ekman	Örebro, Tullängskolan, Sweden
28. Joanna Sturk	Örebro, Tullängsskolan, Sweden
29. Lisa Sevón	Örebro, Tullängskolan, Sweden
30. Niclas Andersson, Sebastian Jacobson, Andreas Börjesson	Örebro, Tullängskolan, Sweden
31. David Hedberg	Örebro, Tullängsskolan, Sweden
32. Bahadir Güngör	Örebro, Tullängskolan, Sweden

Send any comments or questions to: David Pleacher